Asymptotic analysis of high frequency modes for thin elastic plates

Abstract

In this paper, we show that the high frequency modes of a thin clamped plate and the associated eigenfunctions converge, as the thickness of the plate goes to zero, to the eigenvalues and the eigenfunctions of a two-dimensional eigenvalue problem associated to the stretching displacements of the plate.

Keywords

• linear elasticity
• asymptotic analysis
• thin plates
• eigenvalue problem
• high frequency modes
• stretching vibrations